1993 Fiscal Year Final Research Report Summary
Research of mathematics for statistical inference and its applications
| Project/Area Number |
04302010
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| Research Category |
Grant-in-Aid for Co-operative Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kagoshima University |
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Principal Investigator |
YAMATO Hajime Kagoshima Univ., Dept.of Math., Professor, 理学部, 教授 (90041227)
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| Co-Investigator(Kenkyū-buntansha) |
YANAGAWA Takashi Kyusyu Univ., Dept.of Math., Professor, 理学部, 教授 (80029488)
TANAKA Yutaka Okayama Univ., Dept.of Statist., Professor, 教養部, 教授 (20127567)
TANAKA Kensuke Niigata Univ., Dept.of Math., Professor, 理学部, 教授 (70018258)
KAGEYAMA Sanpei Hiroshima Univ., Dept.of Math., Professor, 学校教育学部, 教授 (70033892)
INAGAKI Nobuo Osaka Univ., Dept.of Math., Professor, 基礎工学部, 教授 (10000184)
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| Project Period (FY) |
1992 – 1993
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| Keywords | Likelihood / Experimental design / Nonparametric inference / Multivariate analysis / Time series analysis / Bio-statistics / Sequential analysis / Non-normal distribution |
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| Research Abstract |
In order to solve many mathematical problems concerning the statistical inference and its applications, we have nationwide meetings for the follwing themes. (1) Statistical models with parameters and inference by likelihood : We had many results for inference by likelihood with exponential families and another statistical models. (2) Theory of experimental design and its applications : Many results for experimental designs and combinatorial theory were reported and discussed. (3) Recent development of nonparametric inference and its applications : New developments of nonparametric inference, time series analysis and related topics were reported. (4) Theory of optimization and its applications : Many problems of mathematical programming and the related fields were studied. (5) Theory of multivariate analysis and its applications : Multivariate growth curve model, likelihood ratio test and other multivariate statistical inference were discussed. (6) Theory of recent time series analysis and its application : We had many results for time series analysis, prediction theory and their applications. (7) Mathematics for bio-statistics and its applications : Statistical inference for medicine and biology were studied. (8) Statistical inference and sequential analysis : Statistical methods for unfixed sample size were discussed. (9) Theory of statistical inference and its optimality : Asymptotic properties of statistics for nonparametric inference and time series analysis were reported. (10) Statistical inference for non-normal distributions and its applications : Properties of statistics associated with estimations and tests were discussed for non-normal distributions. (11) Theory of multivariate analysis and computer : Statistical methods using computer were reported. (12) Theory of statistical experiment and its applications : For statistical experiments, information losses, locally asymptotic normalities and the related topics and studied.
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